The world number one looked out of sorts before rallying, leading 6-7 (7-9) 6-7 (2-7) 6-1 6-0 4-0 when the Italian retired with an injury.
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The decision comes after the No. 2-ranked player in the world pulled out of the French Open last week, citing her mental health.
Having come into the tournament with low expectations, Williams had looked solid through her first three matches, and, with big names falling by the wayside, the American surged up the list of title favourites.
The 39-year-old Swiss prevailed 7-6 (7-5), 6-7 (3-7), 7-6 (7-4), 7-5 over Dominik Koepfer on Saturday night.
But the early departure of seeded players in the women’s tournament continued as third-seeded Aryna Sabalenka was upset by Anastasia Pavlyuchenkova in the third round.
The Russian tennis player arrested on suspicion of match-fixing at last year’s French Open was released from police custody on Friday, judicial officials told The Associated Press.
The 2019 champion trailed 6-1, 2-2 in the second round when she signaled she was not able to keep playing against Polish opponent Magda Linette on Court Philippe Chatrier.
Williams is aiming to tie the record of 24 grand slam titles currently held by the great Margaret Court.
Osaka had been fined $15,000 for refusing to fulfil her media commitments after a 6-4 7-6 (4) first-round victory over Patricia Maria Tig.
The Japanese player has been fined £12,900 (€15,000) after deciding to boycott press conferences at the tournament. Osaka announced on Wednesday that she would not be conducting press conferences at the tournament, which began on Sunday and runs until May 13.
The Spaniard recovered from a potentially dangerous fall after tripping over a raised line to take the latest installment of the most-played rivalry in modern men’s tennis.
World number two Nadal claimed his fourth Laureus award as he was recognised for his 13th French Open and record-equalling 20th major.
Federer, 39, is making his comeback after two knee operations and has not played a Grand Slam since January 2020.
France President, Emmanuel Macron, announced on 31 March that a schedule for the return of sporting events would start from mid-May onwards, which led to the decision by the French Tennis Federation.
The world No 2, who won his 20th Grand Slam title at the French Open earlier this month, has decided to prolong his season despite saying earlier this month that he was unsure whether he would be back on a match court in 2020.
With his record-improving 13th triumph at Roland Garros, world number two Nadal is now tied with Swiss Roger Federer as the player with the most men’s singles major titles.
The 19-year-old crushed Sofia Kenin 6-4 6-1 to crown an extraordinary fortnight.
Djokovic looked to be easing to a relatively-straightforward victory when he served for the match at 5-4 in the third set only for Tsitsipas to save a match point and turn the contest completely around
The Moscow-born Florida-based 21-year-old gave a masterclass of game management on a windy Court Phillipe Chatrier and will face Polish teenager Iga Swiatek on Saturday
The shocking win helped the Argentine to reach his first Grand Slam semi-final